AI 中文总结
研究双缝实验中量子粒子干涉效应的经典概率描述，通过复标量场经典场论，利用守恒荷定义粒子子系统，将概率信息编码在复波函数中，实现其时间演化服从薛定谔方程，可产生多种典型量子效应。
AI 中文摘要
我们展示了双缝实验中量子粒子的干涉效应如何能用经典概率来描述。我们研究了具有概率初始条件的复标量场的经典场论。一个核心要素是守恒荷，它引出了粒子的概念。这些是描述场构型概率分布性质的统计可观测量。守恒荷定义了真空态粒子激发的子系统。我们将单粒子子系统的概率信息编码在一个复波函数中。经典概率分布的刘维尔方程意味着这个波函数的时间演化服从量子粒子在势场中的薛定谔方程。该势源于相对论性经典场论中质量项的空间依赖性。它可以任意选取，从而实现干涉、隧穿或离散能谱等典型量子效应。
英文摘要
We demonstrate how the interference effects for a quantum particle in the double-slit experiment can be described by classical probabilities. We investigate a classical field theory for a complex scalar field with probabilistic initial conditions. A central element are conserved charges leading to the concept of particles. These are statistical observables which describe properties of the probability distribution for field configurations. The conserved charges define subsystems for particle excitations of a vacuum state. The classical probability distribution for the one-particle subsystem can be expressed in terms of a complex wave function. The Liouville equation for the classical probability distribution implies that the time evolution of this wave function obeys the Schrödinger equation for a quantum particle in a potential. The potential arises from space-dependent external fields in the otherwise relativistic classical field theory. It can be chosen arbitrarily, realizing the typical quantum effects of interference, tunneling or discrete energy spectra.
CommentsAdditional discussion of one-particle observables, 16 pages
